A187042 -id:A187042 - cp's OEIS frontend

A378494 Intersection of A000379 and A026424.

8, 12, 18, 20, 27, 28, 32, 44, 45, 48, 50, 52, 63, 68, 75, 76, 80, 92, 98, 99, 112, 116, 117, 120, 124, 125, 147, 148, 153, 162, 164, 168, 171, 172, 175, 176, 188, 207, 208, 212, 236, 242, 243, 244, 245, 261, 264, 268, 270, 272, 275, 279, 280, 284, 292, 304, 312, 316

Offset: 1

Paolo Xausa, Nov 28 2024, following a suggestion from Peter Munn

nonn

First differs from A187042 at n = 24, where a(24) = 120 is missing from A187042.

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. A000379, A026424, A187042, A378489.

A000379Q[k_] := k == 1 || EvenQ[Count[IntegerDigits[FactorInteger[k][[All, 2]], 2], 1, 2]];
A026424Q[k_] := OddQ[PrimeOmega[k]];
Select[Range[500], A000379Q[#] && A026424Q[#] &]

A241270 Numbers with the property that in their factorization over distinct terms of A050376, the sums of prime and nonprime terms of A050376 are equal.

Original entry on oeis.org

126, 468, 624, 792, 880, 1056, 1150, 2900, 3264, 4606, 5824, 6375, 6624, 8320, 9856, 10388, 11375, 12798, 13650, 16400, 16704, 19250, 20925, 30135, 32625, 36720, 39150, 39900, 53784, 56446, 56925, 57000, 59500, 63455, 65520, 71400, 71500, 72471

Offset: 1

Vladimir Shevelev, Apr 18 2014

nonn

The corresponding sequence of the sum over the primes, which equals the sum over the nonprimes, is 9, 13, 16, 13, 16, 16, 25, 29, 20, 49, 20, 25, 25, 20, 20, 53, 25, 81, 25, 41, 29, 25, 34, 49, 34, 25, 34, 29, 85, 169, 34, 29, 29, 49, 25, 29, 29, 49, ... - Wolfdieter Lang, Apr 25 2014

			126 and 468 are in the sequence since the factorizations are 2*7*9 and 4*9*13 respectively, and 2+7=9, 4+9=13.

V. S. Shevelev, Multiplicative functions in the Fermi-Dirac arithmetic, Izvestia Vuzov of the North-Caucasus region, Nature sciences 4 (1996), 28-43 [Russian].

Peter J. C. Moses, Table of n, a(n) for n = 1..2000
S. Litsyn and V. S. Shevelev, On factorization of integers with restrictions on the exponent, INTEGERS: Electronic Journal of Combinatorial Number Theory, 7 (2007), #A33, 1-36.

Cf. A187039, A187042, A177329, A177333, A177334.

More terms from Peter J. C. Moses, Apr 18 2014

New extension from Wolfdieter Lang, Apr 25 2014

cp's OEIS Frontend

A378494 Intersection of A000379 and A026424.

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